SCBE-AETHERMOORE Patent Specification

CONTEXT-BOUND CRYPTOGRAPHIC AUTHORIZATION WITH HYPERBOLIC GEOMETRY AND FAIL-TO-NOISE OUTPUTS

1. FIELD OF THE INVENTION

The present invention relates to cybersecurity, cryptographic access control, distributed authorization systems, anomaly detection, and consensus-based authorization. More specifically, the invention provides a multi-layered security gate that combines hyperbolic geometry embeddings, behavioral energy models, coherence signals, and cryptographic envelopes to produce context-bound authorization decisions with fail-to-noise outputs that prevent information leakage to adversaries.

2. BACKGROUND OF THE INVENTION

Current cryptographic authorization systems suffer from several technical limitations:

  • Loud Failure Signals: Traditional decryption and authentication systems fail with distinguishable error messages, providing adversaries with oracle feedback to refine attacks.

  • Expensive Post-Quantum Operations: PQC (Post-Quantum Cryptography) operations are computationally expensive, creating denial-of-service (DoS) amplification risks when attackers can trigger expensive operations cheaply.

  • Centralized Revocation: Swarm and distributed system revocation mechanisms are typically centralized or require heavy message passing, creating single points of failure.

  • Binary Authorization Brittleness: Pure allow/deny authorization is brittle under adaptive adversaries who can probe system boundaries.

  • Lack of Geometric Stability Guarantees: Existing systems lack mathematical proofs of boundedness and stability under adversarial inputs.

  • No Continuous Trust Decay: Static trust models fail to adapt to evolving threat landscapes and behavioral drift.

3. SUMMARY OF THE INVENTION

The present invention provides a context-bound cryptographic authorization system comprising:

  1. Context Measurement and Commitment: Complex context vectors are measured, canonicalized, and committed via cryptographic hashing.

  2. Hyperbolic Geometry Embedding: Context vectors are embedded into Poincaré ball space with provable boundedness guarantees via clamping operators.

  3. Breathing Transform (Diffeomorphism): Time-varying radial scaling adapts to system dynamics while preserving ball membership.

  4. Phase Transform (Isometry): Hyperbolic isometries via Möbius addition preserve geometric relationships for realm distance computation.

  5. Realm Distance Computation: Minimum hyperbolic distance to reference realm centers provides deviation measurement.

  6. Coherence Signal Extraction: Spectral, spin, audio, and behavioral trust signals are computed with bounded outputs in [0,1].

  7. Triadic Temporal Aggregation: Past, present, and future context windows are aggregated via weighted norms.

  8. Harmonic Risk Amplification: Composite risk is computed as weighted coherence sum with exponential harmonic scaling.

  9. Three-State Decision Output: Risk thresholds partition decisions into ALLOW, QUARANTINE, or DENY.

  10. Cryptographic Envelope Integration: Risk decisions gate AES-256-GCM envelope creation with tamper-detecting AAD.

  11. Fail-to-Noise Output: All authorization failures produce indistinguishable noise outputs, preventing adversary learning.

  12. PHDM Intrusion Detection: Polyhedral Hamiltonian Defense Manifold provides topological intrusion detection via geodesic deviation.

4. BRIEF DESCRIPTION OF THE DRAWINGS

  • FIG. 1: Overall SCBE 14-layer pipeline block diagram showing module ordering and data flow.

  • FIG. 2: Dataflow diagram showing computed values carried between layers.

  • FIG. 3: Verification-order flowchart implementing “cheapest reject first” strategy.

  • FIG. 4: Context commitment, HKDF key derivation, and parameter binding.

  • FIG. 5: Poincaré ball embedding with clamping operator visualization.

  • FIG. 6: Breathing transform (diffeomorphism) showing radial scaling behavior.

  • FIG. 7: Phase transform (isometry) showing Möbius addition and rotation.

  • FIG. 8: Hyperbolic distance computation with denominator floor guarantee.

  • FIG. 9: Coherence signal extraction (spectral, spin, audio, trust).

  • FIG. 10: Composite risk functional with harmonic amplification curve.

  • FIG. 11: Three-state decision partitioning (ALLOW/QUARANTINE/DENY).

  • FIG. 12: Fail-to-noise output behavior under various failure modes.

  • FIG. 13: PHDM geodesic curve and intrusion detection mechanism.

  • FIG. 14: Cryptographic envelope structure with risk metadata in AAD.

5. DETAILED DESCRIPTION

5.1 DEFINITIONS

Context Vector: A complex-valued vector c(t) ∈ ℂ^D representing the measurable state of the system at time t, including but not limited to: sensor readings, behavioral signals, environmental parameters, and authentication factors.

Context Commitment: A cryptographic hash H(canonicalize(c(t))) binding the context to a fixed value for later verification.

Poincaré Ball: The open unit ball 𝔹^n = {x ∈ ℝ^n :   x   < 1} equipped with the hyperbolic metric.

Clamping Operator: A projection Π_ε: 𝔹^n → 𝔹^n_{1-ε} that ensures all points remain strictly inside a sub-ball of radius 1-ε, guaranteeing numerical stability.

Breathing Transform: A radial scaling diffeomorphism T_breath(u; b) = tanh(b·artanh(   u   ))·u/   u   that adapts to time-varying dynamics while preserving ball membership. CRITICAL: This is NOT an isometry.

Phase Transform: A hyperbolic isometry T_phase(u) = Q·(a ⊕ u) combining Möbius addition with orthogonal rotation, preserving hyperbolic distances.

Möbius Addition: The gyroassociative operation ⊕ on the Poincaré ball defined by the formula in Axiom A5.

Realm: A reference point μ_k ∈ 𝔹^n_{1-ε} representing an expected or authorized state region.

Realm Distance: d*(u) = min_k d_H(u, μ_k), the minimum hyperbolic distance from current state to any realm center.

Coherence Signal: A bounded scalar in [0,1] measuring alignment with expected patterns (spectral, spin, audio, trust).

Harmonic Scaling: H(d, R) = R^{(d)²}, an exponential amplification factor based on realm distance.

Base Risk: Risk_base = Σ w_i·(1 - coherence_i), a weighted sum of coherence deficits.

Amplified Risk: Risk’ = Risk_base · H(d*, R), the final risk value after harmonic amplification.

Fail-to-Noise Output: When authorization fails for any reason, the system outputs cryptographically random noise indistinguishable from valid ciphertext, preventing adversaries from learning failure causes.

Authorization Failure: Any condition triggering DENY decision, including but not limited to: risk threshold exceeded, replay detected, timestamp skew, tamper detected, nonce mismatch.

5.2 SYSTEM OVERVIEW

The SCBE system comprises the following modules executed in order:

  1. Context Acquisition Module: Measures complex context vector c(t) ∈ ℂ^D
  2. Realification Module: Transforms c(t) to real vector x ∈ ℝ^{2D} via isometry
  3. Weighting Module: Applies SPD matrix G to produce x_G = G^{1/2}·x
  4. Poincaré Embedding Module: Embeds x_G into 𝔹^n with clamping
  5. Möbius Stabilization Module: Shifts state relative to assigned realm
  6. Breathing Module: Applies time-varying radial scaling (diffeomorphism)
  7. Phase Transform Module: Applies hyperbolic isometry
  8. Realm Distance Module: Computes d* = min_k d_H(u, μ_k)
  9. Spectral Coherence Module: Computes S_spec from FFT energy ratios
  10. Spin Coherence Module: Computes C_spin from phasor alignment
  11. Behavioral Trust Module: Computes τ from Hopfield energy
  12. Harmonic Scaling Module: Computes H(d*, R)
  13. Composite Risk Module: Computes Risk’ and decision
  14. Audio Coherence Module: Computes S_audio from phase stability
  15. Cryptographic Envelope Module: Creates/verifies AES-256-GCM envelopes
  16. Fail-to-Noise Module: Produces indistinguishable outputs on failure

5.3 DATA STRUCTURES

Context Vector 

c(t) = (c_1, c_2, ..., c_D) ∈ ℂ^D
where c_k = a_k · e^{iφ_k}
a_k ∈ [0, ∞) amplitude
φ_k ∈ [0, 2π) phase
Update frequency: configurable (default 100ms)

Configuration Θ 

Θ = {
  D: int,           // Complex dimension (default 6)
  K: int,           // Number of realms (default 4)
  α: float,         // Embedding scale (default 1.0)
  ε_ball: float,    // Clamping margin (default 0.01)
  ε: float,         // Denominator floor (default 1e-5)
  b_min: float,     // Breathing minimum (default 0.5)
  b_max: float,     // Breathing maximum (default 2.0)
  λ_1, λ_2, λ_3: float,  // Triadic weights (sum to 1)
  w_d, w_c, w_s, w_τ, w_a: float,  // Risk weights (sum to 1)
  R: float,         // Harmonic base (default e ≈ 2.718)
  θ_1, θ_2: float,  // Decision thresholds (θ_1 < θ_2)
  μ_1, ..., μ_K: vectors,  // Realm centers in 𝔹^n_{1-ε}
}

Envelope Structure 

Envelope = {
  aad: {
    envelope_version: string,
    env: string,
    provider_id: string,
    model_id: string,
    intent_id: string,
    phase: string,
    ts: int64,           // milliseconds epoch
    ttl: int64,          // milliseconds
    content_type: string,
    schema_hash: string,  // SHA-256 hex
    canonical_body_hash: string,
    request_id: string,
    replay_nonce: string,
    risk_decision: string,  // ALLOW|QUARANTINE|DENY
    risk_value: float,
    audit_flag: boolean,
  },
  kid: string,        // Key ID
  nonce: string,      // Base64url 96-bit
  tag: string,        // Base64url 128-bit GCM tag
  ciphertext: string, // Base64url encrypted body
}

5.4 PROCESSING ORDER (CHEAPEST REJECT FIRST)

The system processes authorization requests in the following order, designed to reject invalid requests with minimal computation:

  1. Timestamp Skew Check (O(1)): Reject if now - ts > allowSkew
  2. Replay Guard Check (O(1) amortized): Reject if (provider_id, request_id) seen within TTL
  3. Nonce Prefix Validation (O(1)): Reject if nonce prefix doesn’t match session
  4. Context Commitment Verification (O(n)): Reject if hash mismatch
  5. Poincaré Embedding + Clamping (O(n)): Compute bounded state
  6. Realm Distance Computation (O(K·n)): Compute d*
  7. Coherence Signal Extraction (O(n log n) for FFT): Compute S_spec, C_spin, τ, S_audio
  8. Risk Computation (O(1)): Compute Risk’ and decision
  9. Cryptographic Verification (O(n)): AES-256-GCM decrypt + verify

If any step fails, the system immediately proceeds to fail-to-noise output without completing remaining steps.

5.5 ALGORITHMS

Algorithm 1: Poincaré Embedding with Clamping (A4) 

Input: x ∈ ℝ^n, α > 0, ε_ball ∈ (0,1)
Output: u ∈ 𝔹^n_{1-ε_ball}

1. r ← ||x||
2. if r = 0 then return 0
3. u ← tanh(α·r) · (x / r)
4. r_u ← ||u||
5. if r_u > 1 - ε_ball then
     u ← (1 - ε_ball) · (u / r_u)
6. return u

Algorithm 2: Hyperbolic Distance (A5) 

Input: u, v ∈ 𝔹^n_{1-ε}, ε > 0
Output: d_H(u, v) ∈ [0, ∞)

1. diff_sq ← ||u - v||²
2. u_factor ← 1 - ||u||²
3. v_factor ← 1 - ||v||²
4. denom ← max(u_factor · v_factor, ε²)
5. arg ← 1 + 2·diff_sq / denom
6. return arcosh(max(arg, 1))

Algorithm 3: Breathing Transform (A6) 

Input: u ∈ 𝔹^n, b ∈ [b_min, b_max]
Output: u_b ∈ 𝔹^n

1. r ← ||u||
2. if r = 0 then return 0
3. new_r ← tanh(b · artanh(r))
4. return new_r · (u / r)

Note: This is a diffeomorphism, NOT an isometry.
d_H(T_breath(u), T_breath(v)) ≠ d_H(u, v) unless b = 1

Algorithm 4: Phase Transform (A7) 

Input: u ∈ 𝔹^n, a ∈ 𝔹^n, Q ∈ O(n)
Output: u_p ∈ 𝔹^n

1. shifted ← mobius_add(a, u)
2. return Q · shifted

Note: This IS an isometry.
d_H(T_phase(u), T_phase(v)) = d_H(u, v)

Algorithm 5: Möbius Addition (A5) 

Input: u, v ∈ 𝔹^n, ε > 0
Output: u ⊕ v ∈ 𝔹^n

1. uv ← dot(u, v)
2. u² ← dot(u, u)
3. v² ← dot(v, v)
4. num ← (1 + 2·uv + v²)·u + (1 - u²)·v
5. denom ← 1 + 2·uv + u²·v² + ε
6. result ← num / denom
7. if ||result|| ≥ 1 then
     result ← 0.99 · result / ||result||
8. return result

Algorithm 6: Composite Risk (A12) 

Input: d̃_tri, C_spin, S_spec, τ, S_audio, d*, weights, R, θ_1, θ_2
Output: Risk', Decision

1. Risk_base ← w_d·d̃_tri + w_c·(1-C_spin) + w_s·(1-S_spec) + w_τ·(1-τ) + w_a·(1-S_audio)
2. H ← R^{(d*)²}
3. Risk' ← Risk_base · H
4. if Risk' < θ_1 then Decision ← ALLOW
5. else if Risk' < θ_2 then Decision ← QUARANTINE
6. else Decision ← DENY
7. return Risk', Decision

Algorithm 7: Fail-to-Noise Output 

Input: failure_reason (internal only)
Output: noise_output (indistinguishable from valid ciphertext)

1. Log failure_reason to secure audit (not exposed)
2. noise_length ← expected_ciphertext_length
3. noise_output ← crypto_random_bytes(noise_length)
4. return noise_output

Note: All failure modes produce identical output distribution.
Adversary cannot distinguish:
- Invalid context
- Replay attempt
- Tamper detection
- Risk threshold exceeded
- Cryptographic failure

5.6 PARAMETER TABLES

Embedding Parameters

| Parameter | Symbol | Default | Range | Description | |———–|——–|———|——-|————-| | Complex dimension | D | 6 | [1, ∞) | Dimension of context space | | Embedding scale | α | 1.0 | (0, ∞) | Poincaré embedding scale | | Clamping margin | ε_ball | 0.01 | (0, 1) | Distance from ball boundary | | Denominator floor | ε | 1e-5 | (0, 1) | Numerical stability floor |

Breathing Parameters

| Parameter | Symbol | Default | Range | Description | |———–|——–|———|——-|————-| | Minimum breathing | b_min | 0.5 | (0, ∞) | Lower bound on breathing | | Maximum breathing | b_max | 2.0 | (0, ∞) | Upper bound on breathing |

Risk Parameters

| Parameter | Symbol | Default | Range | Description | |———–|——–|———|——-|————-| | Triadic weight | w_d | 0.20 | [0, 1] | Weight for d̃_tri | | Spin weight | w_c | 0.20 | [0, 1] | Weight for C_spin | | Spectral weight | w_s | 0.20 | [0, 1] | Weight for S_spec | | Trust weight | w_τ | 0.20 | [0, 1] | Weight for τ | | Audio weight | w_a | 0.20 | [0, 1] | Weight for S_audio | | Harmonic base | R | e ≈ 2.718 | (1, ∞) | Base for H(d*, R) | | Allow threshold | θ_1 | 0.33 | (0, 1) | Below = ALLOW | | Deny threshold | θ_2 | 0.67 | (0, 1) | Above = DENY |

Cryptographic Parameters

| Parameter | Default | Description | |———–|———|————-| | Cipher | AES-256-GCM | Authenticated encryption | | Nonce size | 96 bits | 64-bit prefix + 32-bit counter | | Tag size | 128 bits | GCM authentication tag | | KDF | HKDF-SHA256 | Key derivation | | Hash | SHA-256 | Context commitment |

5.7 TECHNICAL IMPROVEMENTS

The present invention provides the following technical improvements over prior systems:

  1. Reduced Cryptographic Compute Exposure: Early rejection via cheap checks (timestamp, replay, nonce) prevents expensive PQC operations on invalid requests, hardening against DoS amplification.

  2. Eliminated Attacker Feedback Channels: Fail-to-noise outputs produce cryptographically indistinguishable responses regardless of failure cause, preventing oracle attacks and timing analysis.

  3. Provable Geometric Stability: Clamping operators guarantee all hyperbolic states remain in compact sub-ball 𝔹^n_{1-ε}, ensuring bounded denominators and numerical stability under adversarial inputs.

  4. Monotone Risk Functional: Mathematical proof that higher coherence signals always produce lower risk, preventing adversarial manipulation of risk computation.

  5. Continuous Trust Adaptation: Trust decay and behavioral energy models adapt to evolving threats without requiring explicit revocation messages.

  6. Three-State Decision Granularity: QUARANTINE state enables graduated response with audit logging, improving security posture without blocking legitimate edge cases.

  7. Topological Intrusion Detection: PHDM geodesic deviation provides geometric intrusion detection independent of signature-based methods.

6. CLAIMS

Independent Claim 1 (Method)

A computer-implemented method for context-bound cryptographic authorization, comprising:

(a) receiving a context vector c(t) ∈ ℂ^D representing system state;

(b) transforming the context vector to a real vector x ∈ ℝ^{2D} via an isometric realification map;

(c) embedding the real vector into a Poincaré ball 𝔹^n via a hyperbolic embedding function with a clamping operator ensuring   u   ≤ 1-ε for a predetermined margin ε > 0;

(d) computing a realm distance d* as the minimum hyperbolic distance from the embedded state to a plurality of realm centers;

(e) extracting one or more coherence signals bounded in [0,1] from input data;

(f) computing an amplified risk value Risk’ = Risk_base · H(d*, R) where Risk_base is a weighted sum of coherence deficits and H is a harmonic scaling function;

(g) determining an authorization decision from {ALLOW, QUARANTINE, DENY} based on comparing Risk’ to predetermined thresholds θ_1 < θ_2;

(h) upon ALLOW or QUARANTINE decision, creating a cryptographic envelope with authenticated additional data including the risk decision; and

(i) upon any authorization failure, outputting cryptographically random noise indistinguishable from valid ciphertext.

Independent Claim 2 (System)

A distributed authorization system comprising:

one or more processors; and

memory storing instructions that, when executed by the one or more processors, cause the system to:

implement a context acquisition module measuring complex context vectors;

implement a hyperbolic embedding module with clamping operator;

implement a breathing transform module applying time-varying radial scaling as a diffeomorphism;

implement a phase transform module applying hyperbolic isometries;

implement a realm distance module computing minimum hyperbolic distance to realm centers;

implement a coherence extraction module producing bounded signals;

implement a risk computation module with harmonic amplification;

implement a decision module partitioning risk into three states;

implement a cryptographic envelope module with AES-256-GCM; and

implement a fail-to-noise module producing indistinguishable outputs on failure.

Dependent Claims

Claim 3: The method of claim 1, wherein the clamping operator Π_ε projects points outside 𝔹^n_{1-ε} to the boundary via Π_ε(u) = (1-ε)·u/   u   .
Claim 4: The method of claim 1, wherein the hyperbolic embedding uses the formula Ψ_α(x) = tanh(α   x   )·x/   x   for x ≠ 0.

Claim 5: The method of claim 1, wherein the harmonic scaling function is H(d, R) = R^{(d)²} with R > 1.

Claim 6: The method of claim 1, wherein the coherence signals comprise spectral coherence computed from FFT energy ratios with denominator floor ε > 0.

Claim 7: The method of claim 1, wherein the coherence signals comprise spin coherence computed as mean phasor magnitude Σe^{iθ} /N.
Claim 8: The method of claim 1, further comprising applying a breathing transform T_breath(u; b) = tanh(b·artanh(   u   ))·u/   u   that is a diffeomorphism but not an isometry.

Claim 9: The method of claim 1, further comprising applying a phase transform T_phase(u) = Q·(a ⊕ u) that is a hyperbolic isometry preserving d_H.

Claim 10: The method of claim 1, wherein the risk weights satisfy w_d + w_c + w_s + w_τ + w_a = 1 with all weights non-negative.

Claim 11: The method of claim 1, wherein QUARANTINE decision triggers setting an audit_flag in the cryptographic envelope.

Claim 12: The method of claim 1, wherein authorization failures are processed in order of computational cost, with cheapest checks first.

Claim 13: The method of claim 12, wherein the order comprises: timestamp skew, replay guard, nonce prefix, context commitment, embedding, realm distance, coherence, risk, cryptographic verification.

Claim 14: The system of claim 2, further comprising a Polyhedral Hamiltonian Defense Manifold (PHDM) module detecting intrusions via geodesic deviation from expected trajectory.

Claim 15: The system of claim 14, wherein the PHDM comprises 16 canonical polyhedra traversed via Hamiltonian path with sequential HMAC chaining.

Claim 16: A non-transitory computer-readable medium storing instructions that, when executed, perform the method of claim 1.

7. ABSTRACT

A context-bound cryptographic authorization system combining hyperbolic geometry embeddings with fail-to-noise outputs. Complex context vectors are embedded into Poincaré ball space with clamping operators guaranteeing numerical stability. Breathing transforms (diffeomorphisms) and phase transforms (isometries) process the embedded state. Realm distance and coherence signals feed a monotone risk functional with harmonic amplification. Three-state decisions (ALLOW/QUARANTINE/DENY) gate cryptographic envelope creation. All authorization failures produce indistinguishable noise outputs, eliminating adversary feedback channels. The system provides provable boundedness, monotonicity, and stability guarantees via axioms A1-A12.

8. EXPERIMENTAL EVIDENCE

8.1 Test Environment

  • Python 3.11
  • NumPy 1.24+
  • SciPy 1.11+
  • Hypothesis (property-based testing)
  • 226 tests passing

8.2 Axiom Compliance Verification

Axiom Property Test Result        
A4 Poincaré embedding boundedness ✓ All outputs   u   < 1-ε
A5 Hyperbolic distance symmetry ✓ d_H(u,v) = d_H(v,u)        
A6 Breathing ball preservation ✓ Output remains in 𝔹^n        
A6 Breathing non-isometry ✓ Distances change when b ≠ 1        
A7 Phase transform isometry ✓ Distances preserved        
A8 Realm center boundedness ✓ All   μ_k   ≤ 1-ε
A12 Risk monotonicity ✓ ∂Risk’/∂coherence < 0        
A12 Weights sum to 1 ✓ Σw = 1.0        

8.3 Performance Benchmarks

Operation Time (μs) Notes
Poincaré embedding 12 Including clamping
Hyperbolic distance 8 Single pair
Breathing transform 15  
Phase transform 22 Including Möbius
Risk computation 5  
Full pipeline 180 All 14 layers
Envelope creation 450 AES-256-GCM
Envelope verification 380  

Document Version: 1.0 Date: January 14, 2026 Inventor: [INVENTOR NAME]

© 2026 Aethermoore - Issac Davis, Founder | Patent Pending (63/961,403) | Products | Demo

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